R. Riganti:Physics-Informed Machine Learning for Electronic, Photonic, and Thermal Transport Phenomena

The numerical approximation of partial and integro-differential equations has long served as the foundational engine for predicting complex system behavior and driving engineering design. While traditional numerical techniques, such as Finite Element and Finite Difference methods, provide robust solutions for forward modeling, they frequently encounter severe computational limitations when applied to high-dimensional, multiscale, or inherently ill-posed inverse problems. In regimes characterized by data scarcity, traditional solvers struggle to efficiently resolve inverse tasks like parameter estimation and structural design. Physics-Informed Neural Networks (PINNs) have emerged as a powerful alternative, seamlessly bridging the gap between deep learning and classical physics by embedding physical laws directly into the optimization landscape. By functioning as mesh-free, universal function approximators, PINNs provide a unified framework capable of solving both forward and inverse problems. This dissertation advances the field of Scientific Machine Learning by introducing novel PINN architectures specifically designed to overcome the limitations of classical solvers in photonics, electronics, and heat transport problems. The research focuses on methodological advancements that enabled neural network models to solve complex transport and inverse problems across three distinct physical domains. First, a multiscale PINN architecture is introduced to solve both forward and inverse electromagnetic scattering problems governed by the Helmholtz equation across arbitrary wavelengths. These architectural components recast multiscale PINNs as robust design methods capable of incorporating fabrication constraints in the neural network's outputs, thereby enabling the inverse design of photonic structures. Second, this dissertation addresses integro-differential and Boltzmann-type transport problems through a novel multiscale auxiliary PINN formulation. By leveraging automatic differentiation, this architecture bypasses the numerical errors typically introduced by quadrature rules when evaluating integral operators. Ultimately, this work demonstrates that multiscale auxiliary PINNs enable efficient forward and inverse solutions to equivalent differential problems in photon and phonon transport. Finally, this work presents an architecture for solving the nonlinear Poisson-drift-diffusion equations in semiconductor device modeling. By developing a logarithmic PINN architecture, the coupled model enables the inverse design of silicon device structures from target electric-field profiles. Ultimately, this dissertation demonstrates that embedding physical laws into deep learning architectures circumvents the computational limitations of traditional mesh-based solvers, enabling the solution of forward and inverse design problems across multiphysics domains.